Question

How do you simplify `(1/4)^(-1/2)`?

Answer 1

`2`

Explanation:

We can rewrite this expression as:

`1^(-1/2)/4^(-1/2)`

Since they have a negative sign, flip the fraction and change the exponents positive:

`4^(1/2)/1^(1/2)`

We can then also rewrite it as:

`sqrt(4)/sqrt(1) => 2`

Answer 2

See a solution process below:

Explanation:

First, use these two rules of exponents to rewrite the expression:

`a = a^color(red)(1)` and `(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))`

`(1/4)^(-1/2) => (1^color(red)(1)/4^color(red)(1))^color(blue)(-1/2) => 1^(color(red)(1) xx color(blue)(-1/2))/4^(color(red)(1) xx color(blue)(-1/2)) =>`

`1^(-1/2)/4^(-1/2)`

Now, use these rules of exponents to eliminate the negative exponents:

`x^color(red)(a) = 1/x^color(red)(-a)` and `1/x^color(red)(a) = x^color(red)(-a)`

`1^(-1/2)/4^(-1/2) => 4^(- -1/2)/1^(- -1/2) => 4^(1/2)/1^(1/2) => sqrt(4)/sqrt(1) => 2/1 =>2`